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      <h1>PETSc DMNetwork: Case Studies</h1>
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        <h2>Case Study 1: Power Flow Simulation </h2>

      <p>
        A contingency analysis done on U.S. power
        grid system using an AC power flow model developed using DMNetwork.
        The input file was obtained from the MatPower package
        (<a href="https://matpower.org/">matpower.org</a>). The total numbers of buses,
        generators, loads, and branches are 82,000,
        13,419, 37,755, and 104,121 respectively. The total number of unknowns solved
        is around half a million. Increasing the number of cores from 128 to 2048,
        provided a speedup of twelve.
        <a href="documents/Application1_Betrie_etal-2019_poster.pdf"> Poster</a>
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        <h2>Case Study 2: River Flow Simulation</h2>
      <p>
        A river flow simulation done on the U.S. river
        networks using DMNetwork. The input file was obtained from the NHDPlus dataset
        (<a href="https://www.horizon-systems.com">horizon-systems.com</a>).
        The total numbers of reaches and junctions are 3,098,638 and 3,036,092, respectively.
        The total number of unknowns solved is around half a billion.
        Increasing the number of cores from 1,024 to 65,536, provided a speedup of 35.
         <a href="documents/poster1.pdf">Poster</a>
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